A new derivation considering the non-linear terms has been proposed to calculate stiffness and damping coefficients for short hydrodynamic journal bearings lubricated with pseudo-plastic fluids. The proposed method has relaxed the constraint of small perturbation method applicable to only small values of non-Newtonian factor α. An analytical solution is also given. The non-linear Reynolds equation is solved with a more reasonable boundary condition ∂p*/∂z* = 0 at the location of z*=0 while the analytical pressure distribution is obtained by seven-point Gauss-Legendre integral formula. When the non-dimensional non-Newtonian factor α is small, the stiffness and damping coefficients of computed by the proposed method can agree well with those from small perturbation method, which could verify the proposed derivation. As for large non-dimensional non-Newtonian factor α, the stiffness coefficients $K_{XX}^*$ , $K_{XY}^*$ and $K_{YX}^*$ as well as the damping coefficients $C_{XX}^*$ , $C_{XY}^*$ and $C_{YX}^*$ decrease with the increasing of non-dimensional non-Newtonian factor α. The significance of the derivation is that it can relax the constraint of small α and simplify the computation process.

已提出考虑非线性项的新推导，以计算用假塑性流体润滑的短液动轴颈轴承的刚度和阻尼系数。所提出的方法放宽了仅适用于非牛顿因子α较小值的小摄动方法的约束。还给出了一种分析解决方案。非线性雷诺方程求解以更合理的边界条件∂p * / ∂z在*的位置= 0 ž* = 0，而分析压力分布是通过七点高斯-莱格朗德积分公式获得的。当无量纲非牛顿因子α较小时，所提方法计算的刚度和阻尼系数与小扰动法所求得的刚度和阻尼系数吻合较好，可以验证所提方法的有效性。对于大的无量纲非牛顿因子α，刚度系数 $ K_ {XX} ^ * $ ， $ K_ {XY} ^ * $ 和 $ K_ {YX} ^ * $ 以及阻尼系数 $ C_ { XX} ^ * $ ， $ C_ {XY} ^ * $ 和 $ C_ {YX} ^ * $ 随着无量纲非牛顿因子α的增加而减小。推导的意义在于，它可以放宽对小α的约束并简化计算过程。